Russia "clearly tried to manipulate the outcome" of the 2016 election, Sen. Lindsey Graham said Thursday, and he is drafting a resolution to seek punishment for its actions.

"If [President] Donald Trump forgives [Russian President Vladimir] Putin for what he tried to do in our election, that will scream weakness and the world will get a lot more unstable," Graham told CNN's Kate Bolduan on "At This Hour." "I will never be satisfied until the Congress and the White House work together to punish Russia for trying to interfere with our election."

The current sanctions in Russia are there because of their taking of Crimea, Graham said, and there needs to be new sanctions imposed in response to the U.S. intelligence community's findings that Putin ordered an "influence campaign" be conducted to boost Trump's chances and harm Democratic nominee Hillary Clinton's campaign.

"I'm working with Democrats and Republicans to pass new sanctions," Graham said. "I hope the president will embrace them, because Russia needs to be punished."

Graham noted he is in charge of the Senate Crime and Terrorism Subcommittee, and he plans, along with Democratic ranking member Sen. Sheldon Whitehouse of Maine, to hold an oversight hearing regarding to FBI to try to learn "what Russia actually did" in hopes of validating the intelligence community's findings.

"As a matter of fact I have a resolution I'm drafting now, to be offered soon, that says an attack on one party by a foreign entity is an attack on all parties in the United States," Graham told Bolduan. "We're in this all together. When one party is compromised by a foreign entity, the whole process is compromised."

Graham said if investigations continue to confirm Russia interfered in the election, he will tell the FBI to "go after all things Russian and try to figure out how to prevent this in the future."

Trump, though, has said he'd be open to removing sanctions already filed against Russia to improve relations with Moscow, and that a focus on outside interference in his election was meant to delegitimize his win, reports CNN.